Question

In a clinical trial, 20 out of 881 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 1.9% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 1.9% of this drug's users experience flulike symptoms as a side effect at the α=0.05 level of significance? Because np 0 (1 minus p 0) = 10, the sample size is ▼ less than or greater than 5% of the population size, and the sample ▼ is given to not be random, can be reasonably assumed to be random, cannot be reasonably assumed to be random, is given to be random, the requirements for testing the hypothesis ▼ are are not satisfied. (Round to one decimal place as needed) What are the null and alternative hypotheses? H0: ▼ μ σ p ▼ greater than> equals= not equals≠ less than< versus Upper H 1H1: ▼ μ σ p ▼ greater than> equals= less than< not equals≠ (Type integers or decimals. Do not round.) Several years ago, 43% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,145 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,145 surveyed, 482 indicated that they were satisfied. Construct a 95% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. What are the null and alternative hypotheses? H0: p = ▼ versus H1: p≠ (Round to two decimal places as needed.) Use technology to find the 95% confidence interval. The lower bound is . The upper bound is . (Round to two decimal places as needed.) What is the correct conclusion? A. Since the interval does not contain the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed. B. Since the interval contains the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed. C. Since the interval does not contain the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed. D. Since the interval contains the proportion stated in the null hypothesis, there is sufficient evidence that parents' attitudes toward the quality of education have changed.

Answer 1

pcap = 20/881 = 0.0227

H0: p = 0.019
Ha: p > 0.019

test statistic,
z = (0.0227 - 0.019)/sqrt(0.019*(1-0.019)/881)
z = 0.8044

p-value = 0.2106

as p-value > 0.05, fail to reject H0

#2.
pcap = 482/1145 = 0.4210

SE = sqrt(0.43*0.57/1145) = 0.0146

CI = (0.4210 - 1.96*0.0146, 0.4210 + 1.96*0.0146)
= (0.3924, 0.4496)
Since the interval contains the proportion stated in the null hypothesis, there is insufficient evidence that parents' attitudes toward the quality of education have changed.